Lecture 71 © Jeffrey Bokor, 2000, all rights reservedLecture 7Wave Front AberrationIn a wave-optics picture, the thin lens is represented by phase delay.Which gives Gaussian imaging. Aberrations modify . A spherical lens only gives this in the parax-ial approximation.• For a complex optical system, we can collect the effects of all the lenses and represent them as a phasedelay in the exit pupil. Usually, we subtract the quadratic phase to find the aberration. The residual iscalled the wave front error; or wfe usually depends on the field coordinate. In other words, the aberrations can vary depending onwhere you are in the field of view.Expressed in this way, the primary aberrations are written as:Spherical aberration: Coma: Astigmatism:Field Curvature: Distortion: x, y k–x2y2+2-----------------k x, y–== x, yx2y2+2f-----------------–Wx,y+=Aberration wfe x, yideal wave frontaberrated wavefrontW(x,y)=As4: is normalized radial coordinate in the pupil: image heighthAc3hcosAa2h22cosAd2h2Ath3cosLecture 72 © Jeffrey Bokor, 2000, all rights reservedMonochromatic Aberrations: All of the preceding discussion refers to aberrations that do not depend onwavelength.Chromatic Aberrations: Dependance of wavefront on wavelength.Consider the simple thin lens equation:The index is generally dependent, , so is dependent.Change in image distance: longitudinal chromatic aberration Change in magnification: lateral color. Lateral color is usually more noticeableAchromat: lens designed to cancel chromatic aberration.Lens Design:• The general problem of lens design involves cancelling aberrations• Aberration depends on the lens index, as well as the surface radii.• Complex lens systems can minimize aberrationsSimple singlet case: For a given desired focal length, there is freedom to choose one of the radii for a sin-glet The spherical aberration and coma depend on the particular choice, so these aberrations can be mini-mized by the design form. This is illustrated in the following diagram:1f---n 1–1R1------1R2------–=nn fVioletimageredimageLecture 73 © Jeffrey Bokor, 2000, all rights reservedAchromatic doublet. Two elements made from different glass materialsWe generally choose design an achromat to minimize chromatic aberration across the visible part of thespectrum.R125–=R150–=R1=R150=R125=R116.7=Sphericalaberrationcoma17 field.design: 100mm focal length Optimum form (nearly plano-convex)achromatic doubletpositive element: undercorrected sphericalundercorrected chromaticnegative element: both overcorrected400 500 600 700GFDCViolet Blue Green Yellow Red1.571.561.551.541.531.521.51Different glasses for use inlenses. Fraunhofer designations.C H 656.3 nmD Na 589.2F H 486.1 H 434.0G' nmLFTFSPC2LBC1BSCSensitivity of eyeLecture 74 © Jeffrey Bokor, 2000, all rights reservedDesign of Cemented Doublet AchromatThe ‘D’ wavelength, near the center of visual brightness curve is chosen as the nominal wavelengthfor specifying focal length. We then choose 2 indices on either side, for achromatization, for example,‘C’, and ‘F’. For 2 thin lenses in contactdefine lens power with in meters, units are diopters Define Achromatic design means we make Simplifies to: For normal dispersion has the opposite sign from . One lens must be positive one lens must benegative.For the center of the spectrum (D-line) flint glasscrown glass1fD-----1fD------1fD--------+=prime: crown glassdouble prime: flint glassP1f---=fPPDPDPD+=nD 1–1r1------1r2------–nD 1–1r1--------1r2--------–+=K1r1------1r2------–=K1r1--------1r2--------–=PDnD 1–K= nD 1–K+PFnF 1–K= nF 1–K+PCnC 1–K= nC 1–K+PCPF=nF 1–K nF 1–K nC 1–K nC 1–K+=+KK--------nF nC– nF nC–-----------------------–=KKPD nD 1–K=Lecture 75 © Jeffrey Bokor, 2000, all rights reserved, soCombining results, we find:(1.1) is a property of a given glass called the “dispersion constant” is called the “dispersive power” or V-number. Glass manufacturers spec these numbers for use bydesigners. Now, from Eq. (1.1), (1.2)and (1.3)Eqs. (1.2) and (1.3) are the design equations.PD nD 1–K=KK--------nD 1–PDnD 1–PD---------------------------------=PDPD-----------nD 1– nF nC– nD 1– nF nC–-------------------------------------------------------------––=nD1–nFnC–------------------vPD-----------PD---------+0=PD PD –-----------------=PD P–D
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